Sard Kernel Theorems on Triangular Domains with Application to Finite Element Error Bounds.
Several notes on the circumradius condition
Recently, the so-called circumradius condition (or estimate) was derived, which is a new estimate of the -error of linear Lagrange interpolation on triangles in terms of their circumradius. The published proofs of the estimate are rather technical and do not allow clear, simple insight into the results. In this paper, we give a simple direct proof of the case. This allows us to make several observations such as on the optimality of the circumradius estimate. Furthermore, we show how the case...
Shape preserving rational cubic interpolation.
Simultaneous L1 Approximation of a Compact Set of Real-Valued Functions.
Smooth approximation of data with applications to interpolating and smoothing
In the paper, we are concerned with some computational aspects of smooth approximation of data. This approach to approximation employs a (possibly infinite) linear combinations of smooth functions with coefficients obtained as the solution of a variational problem, where constraints represent the conditions of interpolating or smoothing. Some 1D numerical examples are presented.
Smooth approximation spaces based on a periodic system
A way of data approximation called smooth was introduced by Talmi and Gilat in 1977. Such an approach employs a (possibly infinite) linear combination of smooth basis functions with coefficients obtained as the unique solution of a minimization problem. While the minimization guarantees the smoothness of the approximant and its derivatives, the constraints represent the interpolating or smoothing conditions at nodes. In the contribution, a special attention is paid to the periodic basis system ....
Smooth local interpolation of surfaces using normal vectors.
Smoothing and interpolation in a convex subset of a Hilbert space : II. The semi-norm case
Solving Theodorsen's Integral Equation for Conformai Maps with the Fast Fourier Transform and Various Nonlinear Iterative Methods.
Some algorithm for computing local parameters of quartic interpolatory splines
Some algorithm for testing convexity of histogram
Some algorithms for quartic smoothing splines
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
Some mixed finite element methods on anisotropic meshes
The paper deals with some mixed finite element methods on a class of anisotropic meshes based on tetrahedra and prismatic (pentahedral) elements. Anisotropic local interpolation error estimates are derived in some anisotropic weighted Sobolev spaces. As particular applications, the numerical approximation by mixed methods of the Laplace equation in domains with edges is investigated where anisotropic finite element meshes are appropriate. Optimal error estimates are obtained using some anisotropic...
Some results in multivariate interpolation.
Special curved elements and theitr application [Abstract of thesis]
Spectral approach for kernel-based interpolation
We describe how the resolution of a kernel-based interpolation problem can be associated with a spectral problem. An integral operator is defined from the embedding of the considered Hilbert subspace into an auxiliary Hilbert space of square-integrable functions. We finally obtain a spectral representation of the interpolating elements which allows their approximation by spectral truncation. As an illustration, we show how this approach can be used to enforce boundary conditions in kernel-based...
Spherical basis function approximation with particular trend functions
The paper is concerned with the measurement of scalar physical quantities at nodes on the -dimensional unit sphere surface in the -dimensional Euclidean space and the spherical RBF interpolation of the data obtained. In particular, we consider . We employ an inverse multiquadric as the radial basis function and the corresponding trend is a polynomial of degree 2 defined in Cartesian coordinates. We prove the existence of the interpolation formula of the type considered. The formula can be useful...
Spline recurrences for quartic splines
Spolehlivost numerických výpočtů